Hello Aspirant,

We have

Initial resistance =100 ohm

Final resistance = 500 ohm

Temperature coefficient, α=0.005Ω/ °C

Final temperature = 100 °C

Hey aspirant,

For your given query, i will give you the concept from which your problem will be solved.

Here , it is :

See, the resistance of the conductor changes when the temperature of that conductor changes.

then , new resistance is given by :

R(t) = R(0) [ 1 + alpha  T ]

now , let resistance of bulb filament be R(0) at 0°C

Resistance of the bulb filament at 100°C(R)  = 100ohm

The change in temperature in the first case will be

T = (100°-0°)C = 100°C

Then, resistance is given by above formula , put the values in the above formula then we get :

100 = R(0) [ 1+0.005×100 ]

100 = 1.5 R (0) _________ (a)

The temperature of the bulb filament at R = 200 ohm is T'

Hence, the resistance of the bulb's filament is given by ,

R' = R ( 1+alpha T )

200  = R(o) [ 1+0.005×T' ] ________(b)

Now , divide equation a and b then we get ,

T' = 400°C

I hope this will be helpful for you.

Revert back if i miss something.

Good luck !!!!